p-version least-squares finite element formulation for steady-state two-dimensional turbulent flows using thek-? model of turbulence

✍ Scribed by Bagheri, Masoud ;Surana, K. S.

• Publisher: John Wiley and Sons
• Year: 2000
• Tongue: English
• Weight: 168 KB
• Volume: 16
• Category: Article
• ISSN: 1069-8299
• DOI: 10.1002/(sici)1099-0887(200002)16:2<97::aid-cnm315>3.0.co;2-x

✦ Synopsis

This paper presents a p-version least-squares "nite element formulation for the k} turbulence model. The dimensionless forms of the describing partial di!erential equations are cast into a system of "rst-order partial di!erential equations by utilizing auxiliary variables. Primary, and auxiliary variables are interpolated over an element using equal order C p-version hierarchical interpolation functions. The least-squares error functional is constructed by taking the integrated sum of squares of the errors resulting from the system of "rst-order equations for the entire discretization. The minimization of this least-squares error functional results in "nding a solution vector + , for which the partial derivative of the error functional, with respect to nodal degrees of freedom + ,, becomes zero. This is accomplished by using Newton's method with line search.

Numerical examples are presented for the fully developed and developing two-dimensional turbulent channel #ows utilizing proposed form of the k} model by Launder and Sharma for various Reynolds numbers to demonstrate the convergence characteristics and accuracy of the proposed formulation. The formulation presented here provides a rigorous and assumption-free approach for numerical simulation of turbulent #ows described by complex and highly non-linear partial di!erential equations with special empirical functions. The element error functionals are inherent in the formulation and provide a natural means of hp-adaptive re"nements.